Phase diagram of QCD: the critical point

M. Stephanov

U. of Illinois at Chicago

Phase diagram of QCD: the critical point – p. 1/11

Phase Diagram of QCD

Basic arguments, quark confinement and asymptotic freedom, predict atransition at T ∼ ΛQCD, µB ∼ NcolorΛQCD:

Hadron/resonance gas (π,N , resonances) becomes a (color) plasma of quarksand gluons (ΛQCD ∼ (hadron size)−1).

Simple arguments lead to the sketch:

, GeVBµ

0.1

0 1

T, GeV Quark−Gluon Plasma

hadron gas

vacuum

Asymptotic freedom

quark matter

r ∼ 1/T → 0

K ∼ T

U/K ∼ αs ≪ 1

U ∼ αs/r

K ∼ µ

r ∼ 1/µ → 0

(Fermi gas)

Order of transition?

Originally, arguments suggested 1st order (discontinuous):e.g., SQGP ∼ N2

color, while SHG ∼ N0color.

Phase diagram of QCD: the critical point – p. 2/11

Lattice says: crossover (at µ = 0)Earliest: Columbia group, PRL 65(1990)2491Recent: Wuppertal-Budapest group, Nature 443(2006)675.

Wuppertal-Budapest:

the peak should havegrown 8× for 1st ordertransition

RBC-BI:

0

5

10

15

20

100 200 300 400 500 600 700

0.4 0.6 0.8 1 1.2 1.4 1.6

T [MeV]

s/T3Tr0 sSB/T3

p4: Nτ=46

asqtad: Nτ=6

Entropy/T 3 ∼ # of d.o.f. grows (color isliberated) but no discontinuity

Quarks are important: w.o. them the transition is 1st order.

Phase diagram of QCD: the critical point – p. 3/11

QCD phase diagram (contemporary view)

cros

sove

r

1

0.1

T, GeV

0 µB, GeV

pointcritical

phasesmatterquark

CFLnuclear

mattervacuum

hadron gas

QGP

Models (and lattice) suggest the transition becomes 1st order at some µB .

Phase diagram of QCD: the critical point – p. 4/11

QCD phase diagram (contemporary view)

cros

sove

r

1

0.1

T, GeV

0 µB, GeV

pointcritical

phasesmatterquark

CFLnuclear

mattervacuum

hadron gas

QGP

ESQGP

Color superconductivity

Models (and lattice) suggest the transition becomes 1st order at some µB .

Color superconductivity shapes the landscape at low T , large µB . CFL is the “ice” of QCD.

Phase diagram of QCD: the critical point – p. 4/11

QCD phase diagram (contemporary view)

cros

sove

r

1

0.1

T, GeV

0 µB, GeV

pointcritical

phasesmatterquark

CFLnuclear

mattervacuum

hadron gas

QGP

ESQGP

Color superconductivity

Latticesimulations

Empiricalnuclear physics

Models

αs ≪ 1

Models (and lattice) suggest the transition becomes 1st order at some µB .

Color superconductivity shapes the landscape at low T , large µB . CFL is the “ice” of QCD.

More structure possible/expected. Quarkyonic phase, crystals, critical points, etc.

Phase diagram of QCD: the critical point – p. 4/11

QCD phase diagram (contemporary view)

cros

sove

r

1

0.1

T, GeV

0 µB, GeV

pointcritical

phasesmatterquark

CFLnuclear

mattervacuum

hadron gas

QGP

ESQGP

Color superconductivity

Latticesimulations

Empiricalnuclear physics

Models

neutron stars, quark stars

Heavy ion collisions

αs ≪ 1

Models (and lattice) suggest the transition becomes 1st order at some µB .

Color superconductivity shapes the landscape at low T , large µB . CFL is the “ice” of QCD.

More structure possible/expected. Quarkyonic phase, crystals, critical points, etc.

Phase diagram of QCD: the critical point – p. 4/11

QCD critical point

cros

sove

r

1

0.1

T, GeV

0 µB, GeV

pointcritical

phasesmatterquark

CFLnuclear

mattervacuum

hadron gas

QGP

Phase diagram of QCD: the critical point – p. 5/11

Water

Critical point is a common feature of liquids

Phase diagram of QCD: the critical point – p. 6/11

1822

It took a century to explain the phenomenon of critical opalescence – divergent ξ of densityfluctuations (Smoluchowski). And another 1/2 century to describe critical phenomenaquantitatively – scaling, universality, RG (Landau-Kadanoff-Wilson).

Phase diagram of QCD: the critical point – p. 7/11

Can we discover the QCD critical point?

130

9

5

2

17

50

0

100

150

200

0 400 800 1000 1200 1400 1600600200

T ,MeV

µB, MeV

Freezeout conditions (T ,µB) depend on√

s (GeV)

What is special about the critical point?

It is a point where the thermodynamic functions are singular

Signatures: fluctuations րց near the point non-monotonically vs√

s.

Phase diagram of QCD: the critical point – p. 8/11

Can we discover the QCD critical point?

LR04

LTE03LTE04

LR01LTE08

130

9

5

2

17

50

0

100

150

200

0 400 800 1000 1200 1400 1600600200

T ,MeV

µB, MeV

The lattice has a sign problem to deal with – traditional Monte Carlo does notwork.

Clever methods to circumvent this problem: e.g., reweighting, Taylor expansionin µB , imaginary µB , etc.

Phase diagram of QCD: the critical point – p. 8/11

Can we discover the QCD critical point?

LR04

LTE03LTE04

LR01LTE08

130

9

5

2

17

50

0

100

150

200

0 400 800 1000 1200 1400 1600600200

RHIC scan

T ,MeV

µB, MeV

What do we need to discover the critical point:

Experiments: RHIC, NA61(SHINE), FAIR/GSI

Improve lattice predictions (both algorithm and CPU), understand systematicerrors.

Understand critical phenomena in the dynamical environment of a h.i.c.,develop better signatures

Phase diagram of QCD: the critical point – p. 8/11

Fluctuation signatures of the QCD critical point

Experiments measure for each event: multiplicitiesNπ, Np, . . . , momenta p, etc.

These quantities fluctuate event-by-event.

What is the magnitude of these fluctuations nearthe c.p.? (Rajagopal, Shuryak, M.S.)

M(pT) (GeV/c)0.3 0.4 0.5

Eve

nts

1

10

102

103

104

Universality tells how it grows at the critical point: 〈(δN)2〉 ∼ ξ2.

Correlation length is a universal measure of the “distance” from the c.p.It diverges as ξ ∼ (∆µ)2/5, or (∆T )2/5 as the c.p. is approached

“Shape” of the fluctuations can be also measured and it has even strongerdependence on ξ (arxiv:0809.3450):

〈(δN)3〉 ∼ ξ4.5

, 〈(δN)4〉 − 3〈(δN)2〉2 ∼ ξ7

These moments of the event-by-event distribution measure deviations fromGaussian shape.

As ξ → ∞ the distribution becomes more non-Gaussian.

Phase diagram of QCD: the critical point – p. 9/11

Scan

crossover (̃λ3 = 0)

with max ξ

vs√

s

1st order

freeze-out point

freeze-out points

µB

T

contours ofequal ξ

critical point

Phase diagram of QCD: the critical point – p. 10/11

Concluding remarks

Phase diagram of QCD is full of puzzles and surprises.

The location of the critical point is one of the central unknowns of the QCDphase diagram. Its discovery will transform the phase diagram from theoreticalconjecture to solid knowledge.

The lattice and experiment each have their own challenges. Which approachwill be faster in overcoming them?

Phase diagram of QCD: the critical point – p. 11/11